Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×ΓL(1,𝔽8)⋊C4 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C4×C172) |
| unambiguous semidirect product | Dic7⋊(C3×C172) |
| unambiguous semidirect product | (C17×Dic7)⋊(C3×C17) |
| derived, Sylow | C7 ⋊ C3×C4×C172 |
| Hall | C172×Dic7 ⋊ C3 |
| Hall | C172×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7×C172 ⋊ C3×C4 |
| Hall | Dic7 ⋊ C3×C172 |
| Hall | ΓL(1,𝔽8) ⋊ C4×C172 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8092 |
4046 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 44);